Elliptic curve isogeny class with Cremona label 109263c (LMFDB label 109263.b)

• Label: 109263c
• Number of curves: $2$
• Conductor: $109263$
• CM: no
• Rank: $2$

Rank

The elliptic curves in class 109263c have rank $2$.

L-function data

Bad L-factors:

Prime	L-Factor
$3$	$1 + T$
$7$	$1 - T$
$11$	$1$
$43$	$1 - T$

Good L-factors:

Prime	L-Factor	Isogeny Class over $\mathbb{F}_p$
$2$	$1 + T + 2 T^{2}$	1.2.b
$5$	$1 + 2 T + 5 T^{2}$	1.5.c
$13$	$1 + 13 T^{2}$	1.13.a
$17$	$1 + T + 17 T^{2}$	1.17.b
$19$	$1 + 5 T + 19 T^{2}$	1.19.f
$23$	$1 + 6 T + 23 T^{2}$	1.23.g
$29$	$1 - T + 29 T^{2}$	1.29.ab
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 109263c do not have complex multiplication.

Modular form 109263.2.a.c

Isogeny matrix

The $i,j$ entry is the smallest degree of a cyclic isogeny between the $i$-th and $j$-th curve in the isogeny class, in the Cremona numbering.

$\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)$

Isogeny graph

The vertices are labelled with Cremona labels.

Elliptic curves in class 109263c

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
109263.b2	109263c1	$[1, 1, 1, 36, 276]$	$3869893/24381$	$-32451111$	$[2]$	$26496$	$0.12309$	$\Gamma_0(N)$-optimal
109263.b1	109263c2	$[1, 1, 1, -459, 3246]$	$8036054027/815409$	$1085309379$	$[2]$	$52992$	$0.46966$